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How a good column on the bad lottery fell apart

Writing from Miami, Florida

A recent column in The Wichita Eagle by Randy Scholfield starts out fine, but falls apart near the end. (“Is the lottery the best bet for workers?” February 24, 2006, available at http://www.kansas.com/mld/kansas/news/columnists/randy_scholfield/13945602.htm.)

Mr. Scholfield tells us how the lottery is not a very good bet. He references a survey that tells us how about half of us believe we have a better chance of obtaining a retirement nest egg through winning the lottery rather than by saving and investing.

He then tells us that the large majority of those playing the lottery are poor and don’t have college degrees.

What Mr. Scholfield writes is true. I’d like to illustrate in more detail just how true it is.

Here is how the math works: If you invest $1.00 each week of the year, and you earn 10% on those contributions, at the end of 30 years you will have $9,409. After 40 years you would have $25,316.

These amounts may not seem like much, but you get that for saving just $1.00 per week. If you saved $10.00 each week (I suspect many people spend that much or more on the lottery each week) you would have about $253,000 after 40 years. That’s a significant sum of money.

Plus, if you hold these savings in a Roth IRA, this money will be tax-free when you withdraw it. Lottery winnings are taxed.

Can you earn 10% on your savings? You almost certainly can if you invest these funds in a mutual fund that invests in a broad range of U.S. stocks. That is, invest in an index fund that is based on the S&P 500 index or a broader stock market index. (See Book Review: The Random Walk Guide to Investing.)

The 10% figure is approximately the return of the U.S. stock market over the last 100 or so years. Some years the market goes up more than that, and some years it goes down a lot. But over a long period of time, we can expect returns of about 10%. (If investing in something that has risk concerns you, consider the risk of gambling on the lottery.)

The index fund you select must have low costs. An index fund with high costs will return much less. An index fund that has expenses of 1.5% per year, which some do, would return only $16,682 instead of $25,316 for each dollar invested each week. That’s due to the power of compounding over long periods. You must also select a fund with no sales charges, called a “no-load” fund. If you selected a “load” fund, where part of what you save goes to sales commissions rather than shares of the fund, you might have less than $16,000 rather than the $25,316 you could have by selecting a no-load fund.

(To simply these calculations, I have assumed that you make the contribution for the whole year at the start of the year, rather than a little each week. This doesn’t have much impact on the final figures.)

Now consider the lottery: The average jackpot of the Super Kansas Cash game over the last year was about $360,000. By investing $22 each week as illustrated above, you would have about that much after 40 years.

If you instead spent $22 each week on this game (each play costing $.50, probability of jackpot is 1 in 2,517,200) for 40 years, you would have about a 1 in 28 chance of ever winning the jackpot. Contrast this with the near certainty of the long-term returns of the stock market.

There are other lesser prizes that you would certainly win many of as you made all these bets, and I haven’t considered these prizes. But offsetting these small prizes is the realization that you’d pay income tax on the jackpot from the lottery. The earnings in a Roth IRA, on the other hand, are yours tax-free.

So far, so good for Mr. Scholfield. But then his column takes a downward spiral. We’ll see just how far down it goes in a future post.

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